Struct Multidisc Optim DOI 10.1007/s00158-010-0612-9

INDUSTRIAL APPLICATION

Development of a framework for truss-braced conceptual MDO

Ohad Gur · Manav Bhatia · William H. Mason · Joseph A. Schetz · Rakesh K. Kapania · Taewoo Nam

Received: 3 June 2010 / Revised: 18 October 2010 / Accepted: 10 December 2010 c Springer-Verlag (outside the USA) 2011

Abstract The paper describes the development of a mul- Abbreviations tidisciplinary design optimization framework for con- ceptual design of truss-braced wing configurations. This (·)break break section unconventional configuration requires specialized analysis (·)cr cruise tools supported by a modular and flexible framework to (·)jury jury accommodate different configurations. While the previous (·)root root section framework developed at Virginia Tech was a monolithic (·) main strut Fortran-77 code, the need for more flexibility for com- (·)tip tip section plex truss-braced wing configurations was addressed by (·)wing wing the development of this new framework, which is based on Phoenix Integration ModelCenterTM environment. The Nomenclature framework uses updated structural and aerodynamic de- sign modules that enable a more general geometry defini- A cross-sectional area tion. The new framework, thus, provides a foundation AC load-bearing cross-sectional area for future design concepts, especially multi-member truss- b wing span braced wing configurations. The fuel saving potential of CLα vehicle lift coefficient slope these truss-braced wing configurations is presented by com- c chord paring different truss designs with gradually increased level cavg average chord of complexity. cfuel fuel-tank chord cst wing-box chord Keywords MDO · Truss-Braced Wing · Framework · D drag Design environment dnacelle, lnacelle diameter and length of the engine , respectively E1, E2 Young’s Modulus of the wing skin and webs, respectively (EI)xx,(EI)zz bending stiffness The paper was presented as AIAA Paper 2010-2754 in the 6th AIAA F shear force Multidisciplinary Design Optimization Specialist Conference, s April 12–15, 2010, Orlando, Florida. (GJ) torsion stiffness G , G Shear Modulus of the wing skin and O. Gur (B) · M. Bhatia · W. H. Mason · 1 2 J. A. Schetz · R. K. Kapania spar webs, respectively Virginia Polytechnic Institute and State University, g acceleration of gravity Blacksburg, VA 24061-0203, USA Kg gust alleviation factor e-mail: [email protected] L lift T. Nam M Mach number Georgia Institute of Technology, Atlanta, GA 30332-0150, USA m vehicle mass O. Gur et al. ng gust load factor 1 Introduction q shear flow q0 constant shear flow in the skin to sat- A CONCEPTUAL design is a complex process that com- isfy the requirement of closed-beam bines analyses from a variety of disciplines. The design section environment framework should connect the various dis- qT shear flow in the skins ciplinary analyses while enabling easy replacement and Rel chordwise Reynolds number upgrading of these disciplinary analyses. This is especially SFlaps area true in a case where unconventional air vehicle configu- SFuel,CS cross sectional area of the rations are to be designed requiring generalized analysis Sref reference area modules. This paper describes the development of a Truss- SW wing area Braced Wing (TBW) design framework, concentrating on s non-dimensional coordinate the challenges of modeling and designing this revolutionary Tmax .req maximum required thrust configuration. TSFCcr cruise thrust specific fuel consumption Various descriptions of conceptual-design frameworks TSFCSLS static sea level thrust specific fuel are available in the literature. Each framework puts the consumption emphasis on a different topic. For example, the framework t cross sectional thickness developed by Perez et al. (2006) is concentrated on design- t¯ average skin thickness ing the vehicle control system. Thus, most of the develop- t0, t1 lower and upper locations of the wing ment effort in that was invested towards studying the control skin, respectively system analysis. Mukhopadhyay (2007) reviews several t2 skin thickness of the leading and trail- cases of conceptual design with emphasis on the struc- ing edge spar webs tural analysis. He presents design examples for conventional tnew, told new and old skin thickness, airliners, a Blended Wing Body (BWB) configuration, a respectively High Altitude Long Endurance (HALE), and space vehicles. tstress, tbuckling thickness required to satisfy the stress Antoine and Kroo (2005) concentrate on the noise and emis- and buckling limits, respectively sion analyses, along with an aerodynamic analysis to design u,w transverse and chordwise bending de- environmental-friendly vehicles. formations, respectively During the 1950’s, Pfenninger (1976) proposed the de- V airspeed sign of a truss-braced wing to achieve a reduction in both VG gust velocity the thickness to chord ratio, wing sweep, and an increase Vx , Vz transverse shear forces in the wing span so as to reduce the structural weight, W1, W2, W3 FLOPS wing weight parameters but with complex topology as shown in Fig. 1. Following WBM bending material weight Pfenninger’s lead, the concept of a Strut-Braced Wing Wengine engine weight Wfold wing folding mechanism weight Wi , W f initial and final weight, respectively Wref , lref , dref , Tref weight, length, diameter, and thrust, of reference engine, respectively WSM shear material weight X, Y , Z coordinates α angle of attack ε A axial strain η integration parameter ηc convergence factor ηfold non-dimensional spanwise fold location θ y torsional rotation 0.25 quarter chord sweep μg mass ratio ρ air density σ air density ratio σ A axial stress Fig. 1 One of Pfenninger’s visions (1976) for a truss braced wing σ B longitudinal stress Development of a framework for truss-braced wing conceptual MDO

(SBW) configuration was investigated using Multidisci- minimum TOGW objective function probably represents plinary Design Optimization (MDO) tools (Grasmeyer the most commonly used goal, and emphasizes a lower 1999; Gundlach et al. 2000). The framework used for these life-cycle cost, while the minimum fuel objective function studies was written at the late 1990’s using a monolithic emphasizes lower operational cost and lower emissions. Fortran-77 code. Comparison of the designs resulting from these goals sheds This paper describes the development of a new frame- light on the design limits and trends. The new design envi- work which enables an extended design domain to a multi- ronment enables rapid change of the cost function using the member TBW and other futuristic concepts which include ModelCenterTM drag-and-drop feature. complex topology. To enable treatment of a more general Design constraints are imposed on performance, such topology, a specialized parametric geometry was devel- as: take-off and landing field length, minimum rate-of- oped. The various analysis and design modules were then climb after take-off, single engine flight, etc. Additional written to comply with this new parametric geometry. The constraints are imposed on maximum tip deflection while paper includes a description of these modules with empha- encountering a taxi bump and sufficient fuel capacity as dic- sis on their compatibility to the TBW configuration. In tated by the mission. Again changing the constraints and addition, the need for a modular design environment that their limit values can be done in an easy manner using the supports future developments, leads to the use of Phoenix new design environment. Integration’s ModelCenterTM (2009), which supports such The design variables may include any of the geometric a dynamic and flexible framework. parameters for both the wing and the tail: wing span, wing Last, the paper presents representative results for a min- thickness-to-chord ratios, chords, and sweep; strut/truss imum fuel/emission design problem. The design process length; and some operational variables such as: required was conducted using four different configurations: can- thrust and cruise altitude. tilever, single strut SBW, jury-TBW, and 2-jury TBW. The cross comparison between these configurations empha- 3 Framework description sizes the advantage of TBW airplanes over conventional configurations. Past results (Grasmeyer 1999; Gundlach et al. 2000)forthe TBW design case were obtained using a monolithic code. 2 TBW problem statement This code was written using Fortran 77, and it uses a file based user interface. The outline of the old framework com- The main TBW design requirement is the accomplishment ponents is shown in Fig. 3. The main analyses (propulsion, of a mission which is defined here as flying a range of 14,316 km (7,730 NM) with 305 passengers (see Fig. 2), Baseline Design which is very similar to that of the -200ER. It is assumed that the aircraft has the same as that of a Boeing 777. The aircraft is outfitted with a high-wing inte- Preprocessing grated with truss structures and a T-tail, and is powered by two, high bypass-ratio, turbofan, fuselage mounted engines. Weight Various goals can be considered when designing an air- Convergence vehicle (Jensen et al. 1981; Malone and Mason 1996), Optimizer Propulsion System with an appropriate definition of the objective function for each goal. Possible goals may be one of the following three: minimum Take-Off Gross Weight (TOGW), mini- Aerodynamic mum fuel/emissions, and maximum lift-to-drag ratio. These three figures-of-merits represent different emphases. The

Performance, Structural Design Mach 0.85 Mach 0.85 Cost Function, Module Constraints

Climb 69.44 m/sec (135 kn) Approach Speed Weight Estimation

348 km (350 NM) 3353 m (11,000 ft) 14,316 km (7,730 NM) 3,353 m (11,000 ft) Reserve Range T/O Field Length Range LDG Field Length

Fig. 2 Basic mission used for our design Fig. 3 Old framework components O. Gur et al. aerodynamics, structures, and weight estimation) are in a d. Connecting the old framework to other design frame- weight convergence loop, while the calculation of the design works or additional analysis modules requires a spe- goals and constraints is done as part of the outer optimiza- cially developed interface. tion loop. Although it seems that the various components are independent and modular, the monolithic nature of the These difficulties largely motivated the development of a design framework makes the modifications and updates of new framework using Phoenix Integration ModelCenterTM the analysis modules be a challenging task. Moreover, it environment (2009). The current research uses ModelCenter was written 15 years ago and was modified by a number 9.0 with AnalysisServer 6.0.2. of personnel at different times, which leads to the following The use of ModelCenter environment enables a modu- challenges: lar implementation of various analyses and easy plug-ins of newer analyses and development of interfaces to exist- a. The different modules are merged into one monolithic ing improved ones. Figure 4 shows an image of the N2 code, thus the replacement or even an upgrade of a sin- diagram of the new framework as implemented within the gle component is a difficult task requiring modification ModelCenterTM environment. Main components and con- to the framework source code, thereby increasing the vergence loops are similar to the old framework (Fig. 3), but chances of introducing errors. the actual separation into different modules makes it much b. The configuration handled by the old framework was more flexible and modular. limited only to cantilever and single member strut- The analysis modules were either rewritten using C++ braced wing configurations. Any additional configura- or reused from the old framework (Fortran 77). An effort tions required massive code updates including changes was made to maximize the reuse of existing models, thus to the user interface. avoiding validation of newly written models. However, c. The old framework used a gradient-based optimiza- due to an improved and flexible geometry definition, the tion scheme (Vanderplaats R&D’s DOT (1999)). Other aerodynamics and structures modules were rewritten. optimization schemes are not available within this Analogous to the previous effort (Gur et al. 2009)the framework. new TBW framework contains two iteration loops (see

Fig. 4 New framework N2 diagram Development of a framework for truss-braced wing conceptual MDO

Fig. 3): the TOGW convergence loop and the optimizer ModelCenterTM makes the connection of these modules loop. much easier. The ModelCenterTM environment gives a good The TOGW convergence loop finds the TOGW for a Graphic User Interface (GUI) which support connecting given configuration. This loop contains the following analy- different disciplinary modules into a single multidisci- sis modules. The terms in the parentheses are ModelCenter plinary analysis. module names and can be found in Fig. 4: The outer optimizer loop, presented in Figs. 3 and 4, includes the different optimizer modules such as 1. Engine (EngineWrapper). the Vanderplaats R&D DOT, Design Explorer, etc. 2. Aerodynamic (AeroWrapper). ModelCenter provides a uniform interface across all of 3. Fuel loading (FuelWrapper). these optimizers, which can be used to easily change the 4. Structural Design Module (StructuralWrapper). design variables, cost functions, and constraints. This is a 5. Weight estimation (WeightWrapper). very effective method to quickly change the optimization problem definition and it is used in the current effort in a The engine module finds the engine performance and hybrid mode (see Section 5). geometry properties (see Section 4.3). While the per- formance properties are used later by the perfor- 4 Analysis modules mance module (PerfWrapper, FLOPS_AeroWrapper, and ScrFLOPS_Wrapper in Fig. 4), the engine dimensions As described above the main analysis modules in the current affect the vehicle configuration (size and weight). This framework contain the following: influences the aerodynamic and weight estimation module. The aerodynamic module calculates the lift distribution on a. Structural design. the lifting surfaces (wing, truss members, and tail) and b. Aerodynamic analysis. together with the fuel loading distribution calculated by the c. Propulsion system analysis. fuel module, the total spanwise loading is found. In addi- d. Fuel loading analysis. tion, the aerodynamic module calculates the vehicle drag e. Weight estimation. (See Section 4.2), which is then used by the performance f. Performance analysis. modules. The fuel module, except the fuel loading, cal- culates also the available fuel volume which is used as a Following sections present a detailed description of these design constraint (see Section 4.4). The structural design modules. module uses the aerodynamic and fuel loading as an input and calculates the load bearing mass of the wing system (see 4.1 Structural design module Section 4.1). Finally, the weight estimation module calcu- lates the vehicle TOGW (see Section 4.5). The structural design module calculates the structural For a given set of design variables (configuration, flight weight and deflections of the wing under predefined loading condition) the TOGW is found by iterating over the result- conditions. For a given wing-truss geometric configuration, ing TOGW. The iterations begin with an initial value and aerodynamic load and fuel loading distribution, the struc- go through the aerodynamic analysis, fuel estimation and tural module is used to calculate the minimum amount of structural sizing to calculate the new TOGW. The same cal- material required such that the maximum stress in all struc- culation is repeated in a consecutive iteration with this latest tural members is below the specified material limit and that value of TOGW used as the initial guess. The iterations none of the truss members buckle under a negative 1g are performed until convergence, with a specified maxi- load case. mum number of iterations. Experience with this routine has The structural module is based on a combination of finite shown very good convergence behavior, and with generally element analysis of the wing-truss configuration and the no more than five iterations needed for convergence. Note fully-stressed design criteria. The structure is modeled as that during the TOGW convergence loop, the engine size beam finite elements for wing bending, and bar elements and Center of Gravity (CG) location are iterated. The engine for truss members. The beam elements have four stiffness size influences the vehicle TOGW and drag, and the CG components related to transverse and chordwise bending location influences the trim drag. displacements, axial displacement and torsional rotation. Each of the analysis modules is an independent code, The stiffness is calculated using an equivalent beam model written in C++, Fortran, or Python. In that sense the new of the wing box, as shown in Fig. 5. The upper skin thick- design framework is not different than the previous one, thus ness is assumed to be equal to the lower skin thickness, updating of a single design module is done using the same and the spar web is assumed to have the same laborious approach of coding and debugging. The use of skin thickness as the spar web. The element O. Gur et al.

Fig. 5 Wing and truss member z t =(t/c)c /2 cross-sections are idealized to 1 t be made up of upper and lower t0 2 equivalent skins B A x C D

cst cross-sectional moments of inertia and the load-bearing The material properties assumed for the current study are cross-sectional area, AC , are then calculated as: giveninTable1. A safety factor of 1.5 is used for each load case, and the total loading is a combination of the aerody- AC = 2cst(t1 − t0) + 2t0 · t2 namic lift, fuel inertia loads and self-weight inertia of the t structural elements. 1 3 2 8t0 A total of 19 load cases are considered for structural (EI)xx = 2E cst · z · dz + 2E t 1 2 2 12 sizing: t0   2 3 •+. cst cst 2 5 g pull-up maneuver at 0, 50 and 100% fuel. (EI)zz = 4E1t0t2 + 2E2(t1 − t0) •−. 2 12 1 0 g maneuver at 0, 50 and 100% fuel. • 2 g taxi bump at 100% fuel (does not include aerody- 4(2c t )2 (GJ) = st 1 (1) namic lift). 2 cst + 2 2t1 G1(t1−t0) G2t2 • 6 gust load cases with 0% fuel, and FAR discrete verti- cal gusts specified at different altitudes: 0 ft, 3,048 m where, cst is the wing-box chord, and t0 and t1 are the lower (10 kft), 6,096 m (20 kft), 9,144 m (30 kft) and and upper locations of the wing skin thickness, and t2 is the 12,192 m (40 kft). skin thickness of the leading and trailing edge spar webs. • 6 gust load cases with 100% fuel, and FAR discrete ver- Note that for a sufficiently thin skin, the cross-sectional tical gusts specified at different altitudes: 0 ft, 3,048 m moment of inertia can be approximated as: (10 kft), 6,096 m (20 kft), 9,144 m (30 kft) and 12,192 m (40 kft). 3 ¯2 8t0 (EI)xx = 2E cstt tskin + 2E t (2) 1 2 2 12 The different flight conditions which are used as structural load cases are defined by the flight altitude, Mach number, ¯ where, t = (t1 + t0)/2, and tskin = t1 − t0. Equation (2)is lift coefficient, internal loading (fuel and cargo percentage), consistent with the analysis in previous studies (Gundlach and inertial load factor. Some loading cases are defined as et al. 2000;Gernetal.2005). However, the MDO stud- gust loading cases and are treated accordingly. The gust ies have shown that the optimized wing configurations have loading is derived from a simple one-degree-of-freedom low thickness-to-chord ratios of about 6%, with high skin representation (Pratt and Walker 1955) which consists of a thickness values that warrant a more exact calculation of the gust alleviation factor, Kg: moment of inertia Ixx and that is employed here. . μ The beam finite elements are formulated using Hermite 0 88 g Kg = (3) interpolation functions (Shames and Dym 1985) with the 5.3 + μg cross-sectional properties calculated using (1)and(2) pre- μ sented above. The axial stiffness contribution is calculated where g is the mass ratio: using linear Lagrange interpolation functions for the nodal m axial displacements. The resulting structural finite element μg = (4) 1/2ρS c v C α stiffness matrix is used to calculate the displacements and ref a g L stresses. Multiple components of the stress tensor are calcu- Table 1 Aluminum material (Al-7075 (Dept. of Defense Handbook lated in each part of the wing-box: direct stresses due to both 2003)) properties assumed for current study chordwise and transverse bending, axial stresses, and shear stresses due to both torsion and transverse shear. These Material property Value stresses are then used to calculate the von Mises stress, and Young’s modulus 71.8 × 109 Pa(1.5 × 109 psf) the maximum von Mises stress in each wing-box skin is Poisson ratio 0.33 used to calculate the new skin thickness during the fully- Density 2,883 kg/m3 (180 lb/ft3) stressed design iterations. The iterative procedure is further Max allowable stress 383 × 109 Pa(8.0 × 106 psf) described later in this section. Development of a framework for truss-braced wing conceptual MDO where m is the vehicle mass, Sref is the reference area, cavg obtained and two thickness values, t1 and t2, are defined is the average chord, CLα is the vehicle lift coefficient slope, for each structural finite element. ρ is the air density, and g is the acceleration due to gravity. Note that the fully-stressed design approach dictates that The load factor due to the gust, ng, can be calculated. each element be sized so that it carries the maximum allow-    able stress. Hence, this approach cannot be used to satisfy V 1 V 2 a displacement constraint if the design process involves n = K 1 + G 1 + G (5) g g V α V only structural sizing. The current MDO study involves shape optimization in addition to sizing using the fully- where α is the vehicle angle-of-attack, V is the airspeed, and stressed design approach. A constraint is imposed on the VG is the gust velocity which depends on the flight altitude wing-tip displacement, for which the calculated tip dis- and is based on FAR 25 (Fig. 6). placement value is returned to the optimizer, since it cannot Note that the gate-box limit of 80 m (262.5 ft) is be handled by the structural design routine. The shape opti- addressed by assuming that a folding mechanism can be mizer then changes the shape design parameters to meet the designed to fold the and reduce the parking width displacement constraint. of the aircraft. The folding joint is assumed to be at 40 m The structural sizing approach described in this section (131 ft) on the wing, and an appropriate weight penalty results in a bi-level optimization architecture where the is added as a dead mass at the joint location, follow- upper-level optimizer handles all the geometric design vari- ing the Boeing design for a folding tip option on the 777 ables, and the lower-level optimal design routine (work- (Renzelmann 1993). Further details of the folding wing ing within the structural module) calculates the minimum mechanism weight penalty are given in Section 4.5. structural mass and the resulting deflections for the speci- Skin thickness values for a given wing and truss geom- fied aerodynamic loading. The module calculates the load etry (chord, t/c ratio) are determined based on two criteria: bearing mass of the wing. The other components of the maximum yield stress and buckling load factor. The Euler wing mass (i.e. secondary structure) are estimated using buckling approximation is used for the buckling loads. FLight OPtimization System (FLOPS) developed by NASA Thus, after each fully-stressed design iteration, the new skin (McCullers 1984). thickness values, tnew,aresetto: Note that the deflections calculated by the structural module are later used as a design constraint within the MDO tnew = told + ηc[max(tstress, tbuckling) − told ] (6) process. This means that although the structural module does not constrain the wing deflection directly, the resulting where, tstress is the thickness required to satisfy the stress structural design is a wing-deflection feasible design. limit of the element, tbuckling is the thickness required to satisfy the buckling limit of the member, and ηc is a factor 4.2 Aerodynamic analysis module used to avoid spurious oscillations in the wing mass dur- ing fully-stressed design iterations, that may occur for some The aerodynamic module calculates the drag and structural configurations. The studies use a factor ηc = 0.4. This itera- loading for a given configuration. The drag bookkeep- tion is performed until convergence on the wing mass is ing is based on semi-empirical methods presented in Gur et al. (2010). What follows is a short description of the aerodynamic analysis which is used by the aerodynamic module. 18 The aerodynamic analysis calculates the optimum span- wise aerodynamic load distribution for a given geometry 16 using a Trefftz Plane analysis (Blackwell 1976;Grasmeyer 14 1997). The spanwise loading takes into consideration the truss members, thus the analysis predicts the ideal lift distri- 12 [m/sec] bution in order to maximize the aerodynamic benefit of this q

G-e non-planar configuration. Note that this benefit is less than

V 10 a biplane configuration due to the low clearance between 8 the strut and the wing. In addition to the optimal spanwise lift distribution, this 6 0 5000 10000 15000 analysis computes the minimum induced drag for a given configuration and flight condition. Each flight condition H[m] (representing different load case or performance constraint) Fig. 6 Gust equivalent velocity, source: FAR 25, Section 341 a(5)(i) is defined using the Mach number, flight altitude, and lift O. Gur et al.

Fig. 7 Drag breakdown Drag= Parasite Drag + Induced Drag

Due to Lift Friction/Form Drag Interference Drag Wave Drag Generated Vorticity Shed into Wake Due to intersection Due to Generation geometry of Shock Waves Skin Friction Pressure Drag Additional Profile Sometimes Called Drag Due to Lift Form Drag (Drag from 2-D Airfoils at Lift) Due to Due to Volume Due to Lift Intersection Due to Lift Geometry coefficient. For this set of parameters, the optimized span- Laminar condition) is equivalent to about 0.46 m (1.5 ft), wise loading distribution is calculated and used as input which for a 62.8 m (206 ft) fuselage means practically a for the structural module or for performance calculation fully turbulent fuselage. In addition, riblets can be used, (through the induced drag). Note that longitudinal trim thus the turbulent friction coefficient for the fuselage can around the vehicle CG (calculated in the weight estimation be decreased e.g. decreasing the turbulent skin friction by module) is conducted. This means that the trim drag is also conservative value of 5%. calculated in the lift distribution analysis, thus the resulting The form-factor represents the drag correction due to wing loading distribution reflects a trimmed vehicle. both thickness and pressure drag, which is sometimes re- The induced drag, combined with the friction, wave, and ferred to as the profile drag. Many form-factor models exist interference drag components define the total drag of the (Hoerner 1965; Torenbeek 1982; Jobe 1985;Shevell1989; vehicle configuration. This drag breakdown is presented in Nicolai 1984;Raymer2006), all of them can be used with Fig. 7 and thoroughly described in Gur et al. (2010). the current framework. Separate form-factors models are In what follows, a short summary of this breakdown is used for lifting surfaces and for bodies (fuselage, nacelle). described. Wave drag is a result of the shock waves created over the The friction drag calculation is based on the wetted area vehicle, thus it becomes important at high subsonic speeds. and uses predictions from skin friction models and form- The wave drag model used in this study is based on the Korn factor estimations. The skin friction prediction uses laminar equation extended to swept wings (Mason 1990) with a and turbulent boundary layer models. For laminar flow, Korn factor of 0.95 implying the use of super-critical airfoils the Eckert Reference Temperature method (White 1974) and Korn factor of 0.87 is a conventional airfoil. Along with is used, and for turbulent flow the Van Driest II method (Hopkins and Inoye 1971; Hopkins 1972) (based on the 45 von Kármán–Schoenherr model) is used. The total skin fric- tion coefficient is based on a composite of the laminar/ 40 turbulent flow. Several composite formulas are available (Liu 1972; Collar 1960), and for the current research Schlichting’s composite formula is used (Cebeci and 35 Bradshaw 1977). The complete model for the flat-plate skin friction coefficient can be found in Mason (2009). 30

Different transition criteria are considered through a < < 6 25 TF = 1 Technology Factor (TF) parameter, thus 0 TF 1. This 10 × simple approach is used to determine the chordwise loca- l tion of boundary layer transition. Figure 8 presents two Re 20 curves of transition Reynolds number based on the chord- 15 wise Reynolds number, Rel (taken from Braslow et al. 1990). The dashed curve designated as TF = 0 (technology factor = 0) is for natural laminar flow on standard wings 10 (Boltz et al. 1960). The solid curve, designated as TF = 1, TF = 0 refers to natural laminar flow airfoils (Wagner et al. 1989). 5 The laminar flow is limited to a prescribed chordwise ratio e.g. the chordwise laminar flow is no more than 70% of the 0

0153045 wing chord. V The flat-plate equivalent transition Reynolds number on LE deg the fuselage can also be managed. Note that at cruise con- Fig. 8 Wing transition Reynolds number and technology factor ditions the value of 2.5 × 106 (which represents Aggressive definition Development of a framework for truss-braced wing conceptual MDO

Lock’s fourth-power law (Inger 1993; Hilton 1951; Malone maximum required thrust along the mission and is used as a and Mason 1995), the drag rise, critical Mach number, and design variable during the design process. drag-divergence Mach number can be estimated. The engine module calculates some additional perfor- Interference drag results from the airflow over the inter- mance parameters as well (Leifsson 2005): section of a lifting or truss surface with either the fuselage or with another lifting surface. The fuselage/wing and truss/ 1. Thrust Specific Fuel Consumption (TSFC) at the cruise wing interference drag are modeled using methods sug- condition gested by Hoerner (1965) and drag response surfaces ob- 2. Maximum available thrust, Tavailable, at design cruise tained from viscous Computational Fluid Dynamics (CFD) condition simulations (Tétrault et al. 2001). While the Hoerner model 3. Maximum available thrust, Tavailable, at engine-out con- is relevant for high thickness ratios (>0.4) the CFD response dition. surface is valid for thin wings (<0.075), thus an interpo- lation is done for intermediate thickness ratios (between The cruise TSFC, TSFCcr , depends on the required maxi- 0.075 and 0.4). mum thrust and flight conditions (Mach number, Mcr ,and ) The truss/strut intersections share similar chord length, Outside Air Temperature, OATcr : thus the interference drag is based on drag response surfaces − TSFC = 2.472 × 10 11T 2 − 4.851 obtained from viscous CFD simulations of two similar- SLS max,req −6 chord wings intersection (Duggirala et al. 2009). Here ×10 Tmax,req + 0.5175 again, a thickness-ratio interpolation is done with the TSFC = (TSFC + 0.4021M ) Hoerner model. cr SLS cr 0.4707 Note that the aforementioned models do not include any × (OATcr /OATSL) (8) fairing. According to the literature a fairing is able to reduce the interference drag by at least a factor of 0.1 (Hoerner where TSFCSLS is the static sea level TSFC and OATSL is 1965) and in certain cases even to make the interference the sea level ambient temperature. drag negligible (Shevell 1989;Raymer2006;Hurel1952). The available thrust, Tavailable, is based on the maximum This suggests that a conventional fairing factor is 0.1, and required thrust corrected for the flight conditions (Mach σ aggressive fairing is represented by factor of 0.02. number, Mcr , and density ratio, ):  4.3 Propulsion system analysis module Tavailable =Tmax,req 0.60685 + 0.5344216

2.7981 0.8851778 The engine module is based on a simplified “rubber-engine” × (0.9001142 − Mcr ) σ model which uses a simple formulation. The main purpose of the engine module is to calculate the engine dimensions (9) (nacelle length and diameter) and weight. After calculating the new engine dimensions, the configuration input file is 4.4 Fuel loading module updated, thus the aerodynamic module (which is conducted just after the engine module—see Fig. 3) uses the corrected The fuel loading module calculates the fuel capacity of the nacelle data. wing systems and the fuel loading for the various loading The engine dimensions (engine weight, Wengine, length, cases. lnacelle, diameter, dnacelle) are calculated using a rubber The fuel tanks are defined according to their location engine model, which is based on the following reference inside the lifting-surface members. Note that fuel tanks can parameters (Grasmeyer 1998): be defined for every lifting surface, not just the main wing. Each fuel tank is then defined using several (or single) local T , W = W max req fuel tanks. engine ref T  ref For example, in Fig. 9 a wing constructed of three cross T , sections is defined. Three local tanks are defined as well. = max req lnacelle lref Local-tank 1 is located between cross sections 1 and 2. Tref  Local-tank 2 is also located between cross-sections 1 and 2, T , while local-tank 3 is located between cross sections 2 and 3. = max req dnacelle dref (7) Tank 2 is defined as the merged local-tanks 2 and 3. Tank 1 Tref is defined as local-tank 1. where Wref, lref, dref,andTref are the reference weight, To emphasize the influence of this modeling a schematic length, diameter, and thrust, respectively. Tmax,req is the fuel load distribution is presented in Fig. 9. This loading O. Gur et al.

Tank 1 Using the fuel tank volume the fuel loading due to dif- ferent fuel amounts can be calculated. Note that the struc- Tank 2 tural module uses this loading as a concentrated spanwise load distribution along the mid-chord (aerodynamic-chord) Local line. Tank 1 Local In addition to the fuel inside the lifting-surface tanks, a Tank 2 Local Tank 3 predetermined fuel amount can be considered inside a fuse- lage tank. This fuel is consumed first, thus it is possible that for a certain design the fuselage fuel tank is empty. A repre- sentative fuselage fuel tank contains 17,237 kg (38,000 lb) Cross Section 1 Cross Section 2 Cross Section 3 (similar to the Boeing 777-200ER).

4.5 Weight estimation module 100% Tank 1 dF/dy 100% Tank 2 The weight estimation module calculates the vehicle TOGW. It is based on the FLOPS (McCullers 1984) weight 50% Tank 2 estimation procedure with several improvements:

1. Primary load carrying wing material weight is calcu- lated using the structural design module. Y 2. Folding mechanism weight penalty is added. 3. Fuselage pressurization weight penalty is added. Fig. 9 Example for fuel-tank definition and the resultant fuel loading distribution The wing bending and shear material weight are calculated represents a case which Tank 2 has consumed 50% of its using the structural design module. This weight is then sup- capacity while tank 1 is full. plemented using FLOPS (McCullers 1984) formulas taking The capacity of the fuel tanks is calculated according to into account the secondary wing components (flaps, actua- the geometry defined in the configuration input file. The tors, etc). Figure 11 presents a comparison between Shevell local fuel tanks are defined using the following parameters: (1989) wing-weight index regression line and the current

1. Cross sectional starting point along the lifting surface 70 span. 2. Cross sectional ending point along the lifting surface span. 60 3. Chord ratio—the ratio between the fuel tank chord and the aerodynamic chord. Shevell 50

According to the cross sectional position and the lifting 2 surface geometry, the fuel tank planform is calculated. To kg/m

FLOPS FLOPS find the fuel tank volume, an approximation of the cross W 40 FLOPS / S sectional fuel tank area, S fuel,CS,isused(Raymer2006): W W FLOPS FLOPS B-777 SFuel,CS = 0.85c fuelt (10) 30 B-747

FLOPS MD-80 where c fuel is the fuel tank chord and t is the lifting surface B-707 maximum thickness (Fig. 10). 20

B-727 t 10 B-737 Fuel tank cross section 35 79 cfuel Wing Weight Index kg/m

Fig. 11 Comparison of Shevell (1989) wing weight data and current Fig. 10 Fuel tank cross section wing-weight estimation method Development of a framework for truss-braced wing conceptual MDO weight estimation methods. The vertical axis is the wing Several penalties are then added to the FLOPS weight loading, and the horizontal axis is the wing weight index estimation: which represents the wing geometric properties and the structural loading parameters. The solid line is taken from 1. Main-wing shear material correction. Shevell’s book (p. 392), which was substantiated using var- 2. Truss system structural material. ious air-vehicles data (e.g. DC-8, DC-9, DC-10, 707, 727). 3. Folding-mechanism weight penalty. Two different sets of data points appear on the figure. The 4. Fuselage weight penalty due to pressurization influence. first set is the material weight as calculated using the cur- rent structural design module. The other set of data points is the total estimated wing weight after adding the FLOPS 4.5.1 Main-wing shear material correction additional weight estimation. Most of the vehicles calcu- lated using the current module show good comparison with The shear material weight includes the weight of the spar the results given in Shevell (1989). One exception is the webs and requires a special treatment for the TBW. The 777 data point which represents a more advanced vehi- difference in the sweep angles of the main wing and the cle compared to the other vehicles used to develop the supporting truss structures results in high chordwise (along Shevell correlation. Still, this comparison validates the the airplane longitudinal axis) bending stresses in the spars. current structural weight estimation. Since this phenomenon is absent in conventional cantilever The total wing weight (no fuel or propulsion system) is wings, the shear material calculated from FLOPS cannot be calculated according to the FLOPS equations: used for the TBW weight estimation. A solution might be to remove or factor-out the shear + + material weight from FLOPS and use the remaining as a = TOGWW1 W2 W3 WWing (11) correction to the total (bending and shear) material weight 1 + W1 calculated from the structural design module. However, as where TOGW is the vehicle take off gross weight. Accord- pointed out earlier, it is not possible to directly factor out ingtoFLOPS:1 this weight from FLOPS. Hence, the following procedure is used to calculate the total wing weight. The main-wing (excluding the truss structure) shear Originally, W1 was the wing bending material weight material weight, W , is calculated using the structural including associated nonoptimum weights; W2 was SM analysis. Only the wing bending material (the upper and the spar, and control surface weight; and W3 was for miscellaneous items like fixed leading and trail- lower skins) weight is used to calculate the FLOPS sec- ing edges, wing tips, and . Over the ondary mass correction, which includes a shear material years, these equations have been tweaked so that the weight for a conventional cantilever wing. To factor this representation is not as definitive. Spar and rib mate- out of the FLOPS correction, an estimate of the main- rial weights correlate very well with flap areas—not wing shear material, WSM,est , for a conventional cantilever shear loads. Consequently, they were included with wing is found using the method described in Shanley the control surface weight in term 2. (1960) and Society of Allied Weight Engineers (1996). The final wing weight is then corrected using the difference In the current module, W1,W2, and W3 are calcu- between the calculated and estimated shear material weight, − lated as: WSM WSM,est .

WBM 6.25 4.5.2 Truss system structural material W = 1 + 1 TOGW b This weight is calculated by adding the structural (bend- = . 0.34 · 0.6 W2 0 68SFlaps TOGW ing and shear material) weight of the truss system (for truss = . 1.5 braced wing designs) as calculated by the structural design W3 0 035SW (12) module. where WBM is the primary bending material weight of the main wing as calculated by the structural design module, b 4.5.3 Folding-mechanism weight penalty is the wing span, SFlaps is the flaps area, and SW is the wing area. The folding-wing mechanism is used to allow spans higher than the 80 m (262 ft) gate-box limit. Thus, it is only used 1Private email correspondence with FLOPS’ developer. for configurations with spans over 80 m. Based on an elliptic O. Gur et al. loading distribution the shear force, Fs, acting at the folding FLOPS (McCullers 1984) calculation module. The sim- butt-line is defined as: plified performance module includes the “PerfWrapper” component, and the FLOPS module includes the   “FLOPS_AeroWrapper” and FLOPSWrapper components Fs 1 2 2 2 −1 = 1 − η fold 1 − η − sin η fold TOGW 2 π fold π (Fig. 4). The main output of the performance module is the range (13) covered by the vehicle. The range is used as one of the design constraints, and in most cases it is an active con- where η is the folding position butt line to half span fold straint. In addition, the performance module calculates other ratio. design constraints. The following list contains the various Using (13) and based on the 1,361 kg (3,000 lb) penalty constraints calculated using the performance module. Note of the 6.4 m (21 ft) folding-mechanism of the that the mentioned values are taken from Gur et al. (2009) Boeing 777 (Renzelmann 1993), the estimated weight and represent a Boeing 777-like vehicle. penalty of the folding mechanism, W fold, can be found from: a. Range constraint: the range of the vehicle using its W fold F full fuel capacity is not less than 7,730 NM with an = 0.07 s (14) TOGW TOGW additional 648 km (350 NM) (reserve). b. Initial cruise Rate Of Climb (ROC) constraint: The ROC Note that this model assumes that the weight penalty is pro- at cruise flight conditions and initial cruise weight is portional to the shear force acting on the folding mech- higher than 91.44 m/min (300 ft/min). anism. Two different folding-mechanism weight-penalty c. 2nd segment climb constraint: During takeoff at the sec- models for fighter aircraft are available by York and Labell ond segment conditions (1.2 speed) the climb gra- (1980) and by Raymer (2006). For 777 data, (14)givesa dient should be higher than 2.4% (the requirement for weight penalty of 1,361 kg (3,000 lb), the York and Labell a two engine vehicle according to the Federal Aviation model gives 1,420 kg (3,130 lb), and the Raymer model Regulation, FAR). 1,379 kg (3,040 lb). d. Approach velocity constraint: During the approach con- 2 dition (CL = 1.52, down) the vehicle 4.5.4 Fuselage weight penalty due to pressurization can maintain true airspeed which is less than 68.2 m/s inf luence (132.5 kn). e. Missed approach constraint: During landing missed- 2 The basic fuselage weight estimation is based on FLOPS. approach conditions (CL =1.52, landing-gear up) the Some configurations may reach high cruise altitudes up to climb gradient should be higher than 2.1% (the require- 16,764 m (55,000 ft). This cruise altitude required a heav- ment for a two engine vehicle according to the Federal ier fuselage due to the higher pressure differences between Aviation Regulation, FAR). the cabin and the surrounding atmosphere. A model f. Balanced field constraint: The takeoff and landing bal- described in Torenbeek (1982) is used to modify the FLOPS anced field length is less than 3,353 m (11,000 ft). The calculation. balanced field constraint is calculated according to the In addition to the TOGW, the weight estimation module Roskam (Lan and Roskam 1988) model. calculates the vehicle longitudinal center of gravity, CG. Each module (engine, structural, fuel) calculates the con- The approximate performance module range calculation is tribution of the propulsion system, fuel, and wing bending based on the Breguet range equation.3 material for the weight and CG of the total configuration. V L W Together with the user definition of the fuselage CG, the Range = ln i (15) total CG is calculated. TSFC D W f This CG is then used by the aerodynamic module to cal- / culate the trim drag. Note that the weight estimation module Where V is the airspeed, L D is the lift to drag ratio, Wi is is used after the aerodynamic module, thus the CG location the initial vehicle weight and W f is the final vehicle weight. is updated through the weight convergence loop (Fig. 3). Using a single representative value for the TSFC, lift-to- drag ratio, and velocity, introduces the design altitude as a 4.6 Performance analysis module 2This value represents 1.3 times of the airspeed at stall conditions. A typical value for the stall lift coefficient, CL,max = 2.56, is used. The performance module has two performance calculation 3The TSFC in the following formula is based on fuel weight-flow options: simplified performance calculation module and [lb/hr] rather than mass-flow. Development of a framework for truss-braced wing conceptual MDO design variable which is used to calculate these parameters. range equation suggests a good approximation of the real These parameters are calculated for a 100% cargo and 50% mission performance. For other missions, where the range fuel configuration. is shorter and higher importance is for the climb and takeoff The fuel consumption for the warm-up, taxi, take off, and parts, one should consider using the FLOPS module. climb are considered to be a constant 4.4% of the total fuel weight (Raymer 2006). The current framework enables the use of FLOPS devel- 5 Features of the new framework opedbyNASA(McCullers1984). This performance mod- ule can estimate the mission performance when provided Both the structural design module and the aerodynamic with externally generated aerodynamics, mass properties, analysis are based on the geometric definition of the ana- and propulsion performance data. The FLOPS model was lyzed configuration. While a geometry definition using integrated into the framework as an improved option to the intuitive values (such as span, chord, taper ratio, etc.) is easy approximate mission analysis. An additional aerodynamics to implement for conventional configuration, for more revo- analysis run was also included to generate drag polars in a lutionary configurations, such as TBW, a general hierarchic compatible format required to execute a FLOPS run. These definition is needed. This kind of parametric-geometry is drag polars cover the entire flight envelope of the vehicle, based on node locations which evolve into curves, sections, thus FLOPS can use it in its mission performance analysis. wings, and bodies. The current FLOPS model estimates thrust and fuel flow The old framework which was used for past research by scaling a fixed engine performance model (engine deck) for strut-braced wings (Gur et al. 2009;Grasmeyer1998; provided by NASA. Leifsson 2005; Gundlach et al. 2000;Gernetal.2005) The principal differences between the simplified range was written during the late 1990’s as a monolithic Fortran- estimation and the FLOPS range estimation are highlighted 77 code, and it uses a gradient based Vanderplaats R&D in Fig. 12. The simplified model estimates the amount of DOT optimizer (DOT. Design Optimization Tools 1999). fuel required to climb to the initial cruise with a fixed ratio This framework was extended to TBW cases over the last of TOGW. The range includes only the cruise distance, few years. Using this old framework, an optimized mini- which is computed by the Breguet range equation. The mum TOGW Jury-TBW configuration was found (Gur et al. FLOPS model accounts for fuel needed to complete ground 2009). Figure 13 shows a three-side view of the optimized operation and climb by integrating fuel flow along time configuration. Note that this figure was produced using the steps. In addition, FLOPS range includes all air-distance NASA-developed Vehicle Sketch Pad (VSP), which is an segments including climb and descent. extension of the rapid aircraft modeler (Gloudemans et al. Although the FLOPS module offers a more detailed rep- 1996). The current parametric-geometry can be imported resentation of the mission, the results from the two analyses into VSP, thus enabling a quick visualization of various are in close agreement. In most cases the range differences configurations (Dufresne et al. 2008). Part of the framework are small (less than 3%). This is mainly due to the long development was to introduce this hierarchic parametric- range section of 14,316 km (7,730 NM), thus the Breguet geometry instead of the previous intuitive one, thus

Fig. 12 Comparison of mission T.O & Climb = Simplified Mission Analysis range calculation methods 4.4% of TOGW Altitude Fuel Weight

Average CL & Fixed Mach Cruise

Range

14,316 km (7,730 NM) 648 km (350 NM) Reserve

FLOPS Mission Analysis Altitude Minimum Max. L/D Time-to-Climb Fixed Mach Cruise-Climb Descent

Range

Taxi Out, 9 min 14, 316 km (7,730 NM) 648 km (350 NM) Takeoff, 2 min Reserve O. Gur et al.

Table 2 Old framework geometric parameters

Variable Nomenclature

1WingHalfSpan b/2

2 Wing Quarter Chord Sweep 0.25,wing 3 Wing Center Line Chord cC.L. 4 Wing Center Line Thickness Ratio t/cC.L. 5 Break Butt-Line Ratio ηbreak 6 Wing Break Chord cbreak 7 Wing Break Thickness Ratio t/cbreak 8 Wing Tip Chord ctip 9 Wing Tip Thickness Ratio t/ctip 10 Strut/Wing Vertical Offset Length lstrut/wing 11 Strut Quarter Chord Sweep 0.25,strut 12 Strut Chord cstrut 13 Strut Thickness Ratio t/cstrut 14 Jury/Wing Intersection B.L. Ratio ηjury/wing 15 Jury/Strut Intersection B.L. Ratio ηjury/strut 16 Jury/Wing Vertical Offset Length ljury/wing 17 Jury Chord cjury 18 Jury Thickness Ratio t/cjury 19 Average Cruise Altitude Hcr Fig. 13 Old framework Jury-TBW minimum TOGW design using 20 Takeoff Fuel Weight W f DOT optimizer (Gur et al. 2009) 21 Maximum Required Thrust Tmax,req providing a simple means for unconventional configuration descriptions. The geometric parameters are presented in is now based on the location and properties of the lifting sur- Fig. 14 and Table 2. face cross-sections. The cross sections needed to describe a The current framework does not share the exact same Jury-TBW configuration are presented in Fig. 15. The wing analysis modules, and most of the modules were rewrit- is described using four cross sections (1–4), the main strut ten using C++. Most of the basic fundamental building using three sections (5–7), and the jury is described using blocks were kept, thus the old and new frameworks share two cross sections (8 and 9). The geometric parameters that some of the original Fortran code. In addition, the main are used for the new framework are listed in Table 3. upgrade was the geometric hierarchic representation which The geometric parameters in Table 2 are designated as high-level or intuitive geometric parameters. These are con-

ventional geometric parameters which have sound meaning V for the vehicle configuration. Table 3 presents the cur- cC.L., t/cC.L. 0.25,wing rent low-level or primitive geometric parameters. These have arbitrary geometry meaning according to the used

cbreak, t/cbreak parametric-geometry. The wing sweep definition can de- ctip, t/ctip monstrate the difference. While the standard design pro- . ηbreak b/2 cess uses wing quarter-chord sweep as one of its design b/2 variables, the current design environment uses the X coordi-

nates of the wing tip section. The sweep angle is considered η .b/2 V as a high-level or intuitive geometric parameter, while the jury/wing c , t/c , strut strut 0.25,strut wing section X coordinate is considered low-level or primi- tive geometric parameters. Note that the two sets of parame- cjury, t/cjury lstrut ters (low and high levels) merely represent a different way to l jury define a given configuration. This means that one can create a set of low level parameters, given a set of high level and . . ηjury/strut ηjury/strut b/2 vice-versa. In the new framework the high level geometric parameters are mere derived parameters, depending on the Fig. 14 Old framework geometric description low level geometric parameters. Development of a framework for truss-braced wing conceptual MDO

Fig. 15 New framework of the wing root (X1, X-coordinate of Section 1) and wing Jury-TBW geometric tip (X4, X-coordinate of Section 7), the longitudinal loca- description tions of the other sections (X2 and X3) on the main wing are calculated through linear interpolation between X1 and X4. It is important to note that the primary motivation in 23 1 4 development and use of the new parametric-geometry is its 7 ability to represent complex topologies with great ease; a 9 6 5 8 feature that would be extremely difficulty to achieve with the conventional definitions of sweep, span, etc. All analysis wrappers are capable of dealing with this parameterization It seems that the use of such primitive geometric param- without any modification. As a result, any complexity in the eters gives scant notion of the wing planform, still it is truss-topology (number of members, their relative arrange- capable of describing much more elaborate configurations ment, size, orientation, etc.) can be quickly made through and gives high flexibility in the design space. a single input file, as demonstrated with the examples in Note that the number of geometric parameters, which the paper. This greatly improves the applicability of the describe the same geometry (Tables 2 and 3) remained 21, same analysis tools for simple cantilever configuration or thus the dimensions of the design space did not change for increasingly complex TBW topologies. between the two representations, while the flexibility of This can be demonstrated using the example of a 2-Jury- defining new configurations was improved. TBW configuration (Fig. 16). The configuration adds one It can be seen from Table 3 that the design variables more jury member to the truss-topology, which increases are assigned to a selected set of geometric parameters, like the number of cross sections from 9 (in case of a single- chord, and thickness ratio. The properties of all other param- jury TBW—Fig. 15)to13(Fig.17). Likewise, the number eters needed to completely define the geometry are obtained of design variables needed to optimize this configuration through interpolation or design variable linking, and are increases to 26 (Table 5), compared to 21 for the single-jury giveninTable4. For example, the quarter-chord-line sweep TBW configuration (Table 3). Definition of this expanded angle of the entire main-wing is held constant. Since this optimization problem in the new framework took only about sweep angle is determined from the longitudinal locations 2 h of work. To put this in perspective, the time required to define an optimization problem for a one-jury TBW airplane Table 3 New framework Jury-TBW geometric parameters configuration in the old framework took about three weeks. Variable Nomenclature This is attributed to the fact that the old framework was specifically made to handle only the cantilever and SBW

1 Cross section 1 chord c1 configurations using design variables that defined quantities 2 Cross section 1 thickness ratio t/c1 very specific to them. This example underlines the impor- 3 Cross section 2 Y coordinate Y2. tance of building generality and flexibility into a tool so that 4 Cross section 3 Y coordinate Y3 it can easily address a large set of problems. 5 Cross section 3 chord c3 Different parametric-geometry methods influence the 6 Cross section 3 thickness ratio t/c3 analysis modules rather the optimization process. The same TM 7 Cross section 4 X coordinate X4 ModelCenter design environment can use either the high 8 Cross section 4 Y coordinate Y4 or low level geometric parameters, but the analysis modules 9 Cross section 4 chord c4 are very different. For the new framework, analysis mod- 10 Cross section 4 thickness ratio t/c4 ules were written in the same way as the old framework, thus the above comparison is valid and represents the main 11 Cross section 5 X coordinate X5 advantage of using the low-level geometric parameters. 12 Cross section 5 chord c5 Note that the time to initially set-up a design problem 13 Cross section 5 thickness ratio t/c5 with a new TBW topology comprises of two steps. The 14 Cross section 6 Y coordinate Y6 first step comprises of defining the topology of the TBW, 15 Cross section 7 Z coordinate Z7 where the new geometry is defined in the input file, and 16 Cross section 8 chord c8 the relevant geometry, material and performance parame- 17 Cross section 8 thickness ratio t/c8 ters are specified. These parameters define a superset out 18 Cross section 9 Z coordinate Z9 of which some or all can be defined as design variables. In 19 Average Cruise Altitude Hcr the second step, the selected design variables are defined in 20 Takeoff Fuel Weight W f ModelCenterTM. The flexibility of the new parameterization 21 Maximum Required Thrust T , max req saves a significant amount of time in the first step, as it does O. Gur et al.

Table 4 New framework Jury-TBW geometric parameters

Variable Design variable Parameter Comment √ 1 Cross section 1 chord Wing root chord √ 2 Cross section 1 thickness ratio Wing root thickness ratio √ 3 Cross section 1 X coordinate X -constant √ 1 4 Cross section 1 Y coordinate Y = 0 √ 1 5 Cross section 1 Z coordinate Z = 0 √ 1 6 Cross section 2 chord Interpolation between c and c √ 1 3 7 Cross section 2 thickness ratio Interpolation between t/c and t/c √ 1 3 8 Cross section 2 X coordinate Constant sweep, interpolation between X and X √ 1 4 9 Cross section 2 Y coordinate Jury/Wing spanwise location √ 10 Cross section 2 Z coordinate Z = 0 √ 2 11 Cross section 3 chord Wing break chord √ 12 Cross section 3 thickness ratio Wing break thickness ratio √ 13 Cross section 3 X coordinate Constant sweep, interpolation between X and X √ 1 4 14 Cross section 3 Y coordinate Break and Strut/Wing spanwise location √ 15 Cross section 3 Z coordinate Z = 0 √ 3 16 Cross section 4 chord Wing tip chord √ 17 Cross section 4 thickness ratio Wing tip thickness ratio √ 18 Cross section 4 X coordinate Control the wing sweep √ 19 Cross section 4 Y coordinate Wing half span √ 20 Cross section 4 Z coordinate Z = 0 √ 4 21 Cross section 5 chord Strut chord √ 22 Cross section 5 thickness ratio Strut thickness ratio √ 23 Cross section 5 X coordinate Control strut sweep √ 24 Cross section 5 Y coordinate Y = 0 √ 5 25 Cross section 5 Z coordinate Z -constant √ 5 26 Cross section 6 chord Constant chord, c = c √ 6 5 27 Cross section 6 thickness ratio Constant thickness, t/c = t/c √ 6 5 28 Cross section 6 X coordinate Constant sweep, interpolation between X and X √ 5 7 29 Cross section 6 Y coordinate Jury/Strut spanwise location √ 30 Cross section 6 Z coordinate Constant dihedral, interpolation between Z and Z √ 5 7 31 Cross section 7 chord Constant chord, c = c √ 7 5 32 Cross section 7 thickness ratio Constant thickness, t/c = t/c √ 7 5 33 Cross section 7 X coordinate Strut/Wing intersection, X = X √ 7 4 34 Cross section 7 Y coordinate Strut/Wing intersection, Y = Y √ 7 4 35 Cross section 7 Z coordinate Control the Strut/Wing vertical offset √ 36 Cross section 8 chord Jury chord √ 37 Cross section 8 thickness ratio Jury thickness ratio √ 38 Cross section 8 X coordinate Jury/Strut intersection, X = X √ 8 6 39 Cross section 8 Y coordinate Jury/Strut intersection, Y = Y √ 8 6 40 Cross section 8 Z coordinate Jury/Strut intersection, Z = Z √ 8 6 41 Cross section 9 chord Constant chord, c = c √ 9 8 42 Cross section 9 thickness ratio Constant thickness, t/c = t/c √ 9 8 43 Cross section 9 X coordinate Jury/Wing intersection, X = X √ 9 2 44 Cross section 9 Y coordinate Jury/Wing intersection, Y = Y √ 9 2 45 Cross section 9 Z coordinate Control the Jury/Wing vertical offset Development of a framework for truss-braced wing conceptual MDO

Table 5 2-Jury-TBW design variables

Variable Nomenclature

1 Cross section 1 chord c1 2 Cross section 1 thickness ratio t/c1 3 Cross section 2 Y coordinate Y2. 4 Cross section 3 Y coordinate Y3 5 Cross section 4 Y coordinate Y4 6 Cross section 4 chord c4 7 Cross section 4 thickness ratio t/c4 8 Cross section 5 X coordinate X5 9 Cross section 5 Y coordinate Y5 10 Cross section 5 chord c5 11 Cross section 5 thickness ratio t/c5 12 Cross section 6 X coordinate X6 13 Cross section 6 chord c6 14 Cross section 6 thickness ratio t/c6 15 Cross section 7 Y coordinate Y7 16 Cross section 8 Y coordinate Y8 17 Cross section 9 Z coordinate Z9 18 Cross section 10 chord C10 19 Cross section 10 thickness ratio t/c10 Fig. 16 2-Jury-TBW configuration 20 Cross section 11 Z coordinate Z11 21 Cross section 12 chord C12 22 Cross section 12 thickness ratio t/c not require any modification inside the analysis codes and 12 23 Cross section 13 Z coordinate Z their associated wrappers. 13 24 Average Cruise Altitude H This generic parameterization requires introduction of cr 25 Takeoff Fuel Weight W some measures to maintain the geometric feasibility of f T , the resulting configurations, as explained in the following 26 Maximum Required Thrust max req example. Consider a planar wing shown in Fig. 18.The tip Y - location is always outboard of the break location. However, since the design variables are defined as inde- pendent locations, the design space includes configurations For design points that do not comply with (16), the where the Y location is inboard of Y . This is prevented by preprocessing module produces a new configuration which 2 1 = + ε ε introducing geometric-constraints defined as: consists of Y2,new Y1 ,where is a small value. This configuration is now physically feasible and can be ana- lyzed. In addition, the geometric-constraint is increased by Y2 > Y1 (16) Y1 − Y2, thus the optimization process is penalized due to the geometric infeasible design.

root break tip 2 3 5 1 9 13 8 12 Y1 6 7 Y2 11 10

Fig. 17 2-Jury-TBW cross sections definition Fig. 18 Example for a planar wing design variables O. Gur et al.

6 Minimum fuel/emissions design can be used as a starting design point for a gradient-based optimizer—in the current case the Vanderplaats R&D DOT The main purpose of the TBW design program is to increase is used with its modified feasible direction scheme (DOT. vehicle efficiency, thus saving fuel and decreasing emis- Design Optimization Tools 1999). In this way the optimiza- sions. To explore the fuel saving potential influenced by the tion scheme is a hybrid one which uses the Design Explorer use of a truss configuration, and to emphasize the potential first and then Vanderplaats R&D DOT. of the current framework, four different configurations were This hybrid-optimization scheme is more comprehensive designed using the new framework: cantilever, single SBW, than using a gradient-based optimizer alone. While for the Jury-TBW, and 2 Jury-TBW. use of the gradient-based method, one should find sev- All the configurations assume aggressive laminar flow, eral candidates as an initial design guess, for the hybrid thus TF = 1 with a limit of 70% chordwise laminar flow. method the first optimization scheme finds these candidates The fuselage is considered to be covered with riblets, thus and then the other optimizer (gradient-based method) uses the fuselage skin friction is decreased by 5% from its turbu- these candidates as an initial design point. This makes pos- lent value. In addition, an aggressive fairing is considered. sible the exploration of unconventional design spaces as Global buckling considerations (6) are implied on the demonstrated with the above example. wing parts which are under compression i.e. the inner span- Figure 20 presents the optimized configuration for the wise part of the wing for strut or truss braced configuration. minimum fuel design cases for the cantilever (a), strut- Note that the outer spanwise part of the wing (or the entire braced wing (b), jury truss-braced wing (c), and 2-jury cantilever wing), are not submitted to buckling considera- truss-braced wing (d). The most noticeable feature is the tion, since they are not subjected to compressive loads. change of planform with increased complexity of wing While the old framework uses a single optimization topology. As additional truss members are added, the wing scheme, the new design framework is capable of using span increases and the chord decreases, so the wing aspect different optimizers. One of the available optimization ratio is increased. In addition, the chord of the main strut tools is the Design Explorer developed by Mathematics & is decreased as more truss members are added, and the Engineering Analysis at Boeing Phantom Works. Design strut-wing intersection is pushed towards the wing tip. Explorer uses an orthogonal array design of experiment Note that the was not sized in this effort. (DOE) (Booker 1998) and then builds a response surface The current results use tail dimensions similar to the 777 using Kriging (Audet et al. 2000). These response sur- (although it is a T-tail). In the future additional considera- faces are then used along with a gradient-based optimization tions such as lateral and longitudinal stability will introduce, (Sequential Quadratic Programming—SQP) to find a mini- thus the tail dimensions will be used as design variables. mum. The Design Explorer tool has been successfully used Table 6 presents the active design constraints. All the for optimization problems such as design of a transonic cases exhibit an active range constraint. Note that the range wing (Epstein et al. 2009). constraint, although treated as inequality constraint, is actu- Design Explorer contains features of global optimization ally functions as an equality constraint. i.e. the fuel weight search by keeping multiple local design areas as candidates is calculated to enable the vehicle to accomplish exactly the for the existence of a global minimum. Each of these design predefined mission. For each optimized configuration, the areas is subjected to response surface refinement, thus the additional active constraint indicates the relevant designs optimization procedure works in different design areas, weakness. For cantilever configuration the deflection con- hopefully to find the best one of the various local minimum. straint is the one that limits the wing span. The fuel con- By that, the final local optima found by Design Explorer straint is active for the SBW configuration due to the short

Table 6 Active design constraints Constraint Value Cant. SBW Jury 2-Jury √√√√ Range ≥7,730 NM + 350 NM (reserve) Initial Cruise ROC ≥300 ft/min √√ Maximum section C in cruise ≤0.8 l √ Available Fuel Volume ≥Required Fuel √ Wing Tip Deflection ≤20.3 ft 2nd Segment Climb Gradient ≥2.4% Approach Velocity ≥132.5 KTAS Missed Approach Climb Gradient ≥2.1% Balanced Field Length ≤11,000 ft Development of a framework for truss-braced wing conceptual MDO chord and low thickness ratio of the wing. Due to the even g. Lift-to-drag ratio, L/D. shorter wing chord of the Jury and the 2-Jury configurations, h. Aspect ratio, AR. the maximum cross-sectional lift coefficient constraint is i. Specific wing weight, WW /b. active for both configurations. The design trends are shown in Fig. 20 which presents Note that these parameters are not the design variables but the change of the following parameters for the four different the results of the optimized design. configurations: It is noticeable that as the truss topology complexity increases the fuel weight (cost function) decreases. This a. Fuel weight (the design cost function), WF . happens along increased span and aspect ratio, and de- b. Takeoff gross weight, TOGW. creased wing structural weight. All of these prove the c. Wing weight, WW . benefit of the TBW configuration (Fig. 19). d. Wing area, SW . According to Fig. 20, the best design is the 2-jury TBW e. Strut/wing intersection ratio, ηbreak. which exhibits the lowest fuel weight, along with favorable f. Half span, b/2. values of other parameters. For the 2-jury-TBW, the fuel

(a) Cantilever (b) SBW

(c) Jury-TBW (d) 2-Jury-TBW

Fig. 19 Optimized minimum fuel configurations. a Cantilever, b SBW, c Jury-TBW, d 2-Jury-TBW O. Gur et al.

80 260 60 70 60 40 50 240 tons

tons

tons 40 F W W 30 220 W 20 20 TOGW 10 0 200 0 Cant. SBW Jury 2-Jury Cant. SBW Jury 2-Jury Cant.SBW Jury 2-Jury

750 0.7 60 700 650 0.6 50 600 0.5 40 2

550 0.4 m m 30 W 500 break 0.3 S b/2 450 20 400 0.2 350 0.1 10 300 0 0 Cant. SBW Jury 2-Jury Cant. SBW Jury 2-Jury Cant. SBW Jury 2-Jury

38 28 0.7 36 26 0.6 34 24 32 22 0.5 30 20 0.4 kg/m

AR

L/D 28 18 /b 0.3 26 16 W

W 0.2 24 14 22 12 0.1 20 10 0 Cant. SBW Jury 2-Jury Cant. SBW Jury 2-Jury Cant. SBW Jury 2-Jury

Fig. 20 Trends with the optimized minimum fuel configurations

consumption is 20% less than the cantilever configuration vides access to multiple optimizers, thereby allowing the along with a decrease of 11% in the takeoff weight. The use of hybrid optimization schemes. lift-to-drag ratio is higher by 16%, and the wing weight is The structural design module was developed to deal with less by 18%. Further discussion about the current design generic topology and is based on a finite element formula- problem and some additional insights are available in Mason tion. Ongoing development of this module focuses on the et al. (2010). addition of flutter as an optimization constraint, and that will become a part of the future study. The aerodynamic 7 Conclusions drag estimation module is based on a semi-empirical for- mulation, providing a good balance between computational A new MDO framework for conceptual design of a truss- cost and accuracy of drag estimation for conceptual design. braced-wing configuration is presented. The design space The weight estimation is based on FLOPS statistical models of the TBW configurations is very vast due to the possibil- with additional specialized corrections. The propulsion and ity of a large number of truss topologies. The need to study performance models are based on simplified formulations, a large number of configurations was posed as a fundamen- with the FLOPS analysis as an option. tal requirement behind the development of this framework. One of the main features of the new design environ- A new geometry parameterization scheme was developed ment is the use of hierarchic parametric-geometry, which and detailed in this paper. The details of the disciplinary introduces the use of primitive design variables, thus analyses consistent with this level of generality in design enabling a general definition of highly complex topologies. parameterization are also discussed. While the previous framework was limited to predefined The framework is built on the ModelCenterTM envi- configurations and addition of new members took weeks to ronment that provides an intuitive interface to quickly implement, the new framework can be modified with a new manipulate optimization problem definitions. The frame- configuration in matter of hours. A challenge resulting from work uses updated disciplinary analysis modules with C++ this generic definition that was identified as geometrically wrappers that enable an easy plug-in capability within the infeasible design configurations and a method to overcome ModelCenterTM environment. ModelCenterTM also pro- this using a geometric-constraint was presented. Development of a framework for truss-braced wing conceptual MDO

The framework was used for MDO of multiple TBW DOT. Design Optimization Tools (1999) version 5.0, users manual. configurations. The design studies used minimum fuel con- Vanderplaats Research and Development, Inc., 1767 S. 8th St., sumption as the objective function, and the results show Suite 100, Colorado Springs, CO Dufresne S, Johnson C, Mavris DN (2008) Variable fidelity conceptual that truss-braced wing configurations hold a strong potential design environment for revolutionary unmanned aerial vehicles. to reduce aviation fuel consumption and emissions. Addi- J Aircraft 45(4):1405–1418 tionally, increasing the complexity in truss-topology allows Duggirala RK, Roy CJ, Schetz JA (2009) Analysis of interference larger benefits to be realized. With an increasing number of drag for strut-strut interaction in transonic flow. In: 47th AIAA aerospace sciences meeting including the new horizons forum and truss members, the vehicle efficiency is shown to improve. aerospace exposition. 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All other efforts were limited to Gloudemans JR, Davis PC, Gelhausen PA (1996) A rapid geome- a specific topology or used high fidelity analyses, thus a try modeler for conceptual aircraft. In: 34th AIAA aerospace conceptual design was not available. sciences meeting and exhibit, 15–18 January 1996, Reno, NV. AIAA-1996-0052 Grasmeyer J (1997) A discrete vortex method for calculating the Acknowledgments The authors would like to acknowledge the minimum induced drag and optimum load distribution for air- financial support of NASA Langley Research Center with Dr. Vivek craft configurations with noncoplanar surfaces. VPI-AOE-242, Mukhopadhyadoty as Technical Monitor. Chief scientist Dennis Bush- Multidisciplinary Analysis and Design Center for Advanced Vehi- nell inspired our efforts. 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